Problem: What is the domain of $y=\dfrac{x^3-27}{x+27}$?  (Express your answer using interval notation.)
Answer: The only values of $x$ that would make this fraction undefined are values that makes the denominator $0$. Therefore, the fraction is undefined when $x+27=0$, or when $x=-27$. Hence, the solution is $\boxed{(-\infty,-27)\cup(-27,\infty)}$.